Skip to main content
Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 9, Problema 9.1.8

8. In your own words, what does it mean to say "correlation does not imply causation"? List a pair of variables that have correlation but no cause-and-effect relationship.

Guida verificata passo dopo passo
1
Understand the concept of correlation: Correlation measures the strength and direction of a linear relationship between two variables. It is represented by the correlation coefficient, which ranges from -1 to 1.
Recognize the meaning of 'correlation does not imply causation': This phrase means that just because two variables are correlated (i.e., they move together in some way), it does not necessarily mean that one variable causes the other to change. Correlation only indicates a relationship, not a cause-and-effect connection.
Consider external factors: Correlation can exist due to a third variable (confounding variable) that influences both variables, or it can be purely coincidental. For example, ice cream sales and drowning incidents are correlated, but the underlying factor is the season (summer), which increases both activities.
Identify examples of correlated variables without causation: A common example is the number of movies Nicolas Cage appears in and the number of swimming pool drownings in a given year. These two variables may show correlation, but there is no causal relationship between them.
Reflect on the importance of statistical analysis: To establish causation, researchers must conduct controlled experiments or use advanced statistical methods to rule out confounding variables and demonstrate a direct cause-and-effect relationship.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Correlation

Correlation refers to a statistical measure that describes the extent to which two variables change together. A positive correlation indicates that as one variable increases, the other tends to increase as well, while a negative correlation indicates that as one variable increases, the other tends to decrease. However, correlation does not provide information about the nature of the relationship between the variables.
Video consigliato:
Percorso guidato
05:43
Correlation Coefficient

Causation

Causation implies a direct cause-and-effect relationship between two variables, meaning that changes in one variable directly result in changes in another. Establishing causation typically requires controlled experiments or longitudinal studies to rule out other influencing factors. It is crucial to differentiate causation from correlation to avoid incorrect conclusions about the nature of relationships between variables.
Video consigliato:
Percorso guidato
06:36
Scatterplots & Intro to Correlation

Spurious Correlation

A spurious correlation occurs when two variables appear to be related to each other but are actually influenced by a third variable or are coincidental. For example, ice cream sales and drowning incidents may show a positive correlation during summer months, but both are influenced by the warmer weather rather than one causing the other. Recognizing spurious correlations is essential to avoid misleading interpretations of data.
Video consigliato:
Percorso guidato
05:43
Correlation Coefficient
Pratica correlata
Domanda del libro di testo

"[APPLET] Registered Nurse Salaries In Exercises 27–30, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Adapted from Payscale, Inc.)

27. Correlation Using the scatter plot of the registered nurse salary data shown below, what type of correlation, if any, do you think the data have? Explain.


"

82
views
Domanda del libro di testo

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

9. Slope

a. \(\hat{y}\)_i

b. y_i

c. b

d. (\(\bar{x}\), \(\bar{y}\))

e. m

f. \(\bar{y}\)"

51
views
Domanda del libro di testo

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.

6. Elephant Weight The equation used to predict the weight of an elephant (in kilograms) is

y =- 4016+11.5x_1+7.55x_2+12.5x_3

where x_1 represents the girth of the elephant (in centimeters), x_2 represents the length of the elephant (in centimeters), and x_3 represents the circumference of a footpad (in

centimeters). (Source: Field Trip Earth)

a. x_1 = 421, x_2 = 224, x_3 = 144

b. x_1 = 311, x_2 = 171, x_3 = 102

c. x_1 = 376, x_2 = 226, x_3 = 124

d. x_1 =231, x_2 = 135, x_3 = 86"

36
views
Domanda del libro di testo

In Exercise 25, remove the data for the international soccer player with a maximum weight of 170 kilograms and a jump height of 64 centimeters. Describe how this affects the correlation coefficient r.

42
views
Domanda del libro di testo

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight

loss."

79
views
Domanda del libro di testo

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

12. The point a regression line always passes through

a. \(\hat{y}\)_i

b. y_i

c. b

d. (\(\bar{x}\), \(\bar{y}\))

e. m

f. \(\bar{y}\)"

51
views